An elastic modulus (also known as modulus of elasticity) is a quantity that measures an object or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region:[1] A stiffer material will have a higher elastic modulus. An elastic modulus has the form:
where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some parameter caused by the deformation to the original value of the parameter. If stress is measured in pascals, then since strain is a dimensionless quantity, the units of λ will be pascals as well.[2]
Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are:
- Young's modulus (E) describes tensile elasticity, or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to tensile strain. It is often referred to simply as the elastic modulus.
- The shear modulus or modulus of rigidity (G or ) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as shear stress over shear strain. The shear modulus is part of the derivation of viscosity.
- The bulk modulus (K) describes volumetric elasticity, or the tendency of an object to deform in all directions when uniformly loaded in all directions; it is defined as volumetric stress over volumetric strain, and is the inverse of compressibility. The bulk modulus is an extension of Young's modulus to three dimensions.
Three other elastic moduli are Poisson's ratio, Lamé's first parameter, and P-wave modulus.
Homogeneous and isotropic (similar in all directions) materials (solids) have their (linear) elastic properties fully described by two elastic moduli, and one may choose any pair. Given a pair of elastic moduli, all other elastic moduli can be calculated according to formulas in the table below at the end of page.
Inviscid fluids are special in that they cannot support shear stress, meaning that the shear modulus is always zero. This also implies that Young's modulus for this group is always zero.
In some English texts the here described quantity is called elastic constant, while the inverse quantity is referred to as elastic modulus.
See also[edit]
References[edit]
- ^Askeland, Donald R.; Phulé, Pradeep P. (2006). The science and engineering of materials (5th ed.). Cengage Learning. p. 198. ISBN978-0-534-55396-8.
- ^Beer, Ferdinand P.; Johnston, E. Russell; Dewolf, John; Mazurek, David (2009). Mechanics of Materials. McGraw Hill. p. 56. ISBN978-0-07-015389-9.
Further reading[edit]
- Hartsuijker, C.; Welleman, J. W. (2001). Engineering Mechanics. Volume 2. Springer. ISBN978-1-4020-4123-5.
- De Jong, Maarten; Chen, Wei (2015). 'Charting the complete elastic properties of inorganic crystalline compounds'. Scientific Data. 2: 150009. Bibcode:2013NatSD..2E0009D. doi:10.1038/sdata.2015.9. PMC4432655.
Conversion formulae | |||||||
---|---|---|---|---|---|---|---|
Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these; thus, given any two, any other of the elastic moduli can be calculated according to these formulas. | |||||||
Notes | |||||||
There are two valid solutions. The minus sign leads to .The plus sign leads to . | |||||||
Cannot be used when | |||||||
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Elastic_modulus&oldid=890446931'
Young's modulus | |
---|---|
A given uniaxial stress, whether tensile (extension) or compressive (compression) creates more deformation in a material with low stiffness (red) than with a high stiffness (blue). Young's modulus is a measure of stiffness. | |
E, Y | |
SI unit | pascal |
In SI base units | Pa = kg m−1 s−2 |
Derivations from other quantities | |
Dimension | ML−1T−2 |
Young's modulus or Young modulus is a mechanical property that measures the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in a material in the linear elasticity regime of a uniaxial deformation.
Young's modulus is named after the 19th-century British scientist Thomas Young. However, the concept was developed in 1727 by Leonhard Euler, and the first experiments that used the concept of Young's modulus in its current form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years.[1] The term modulus is derived from the Latin root term modus which means measure.
- 1Definition
- 3Usage
- 4Calculation
Definition[edit]
Linear elasticity[edit]
A solid material will undergo elastic deformation when a small load is applied to it in compression or extension. Elastic deformation is reversible (the material returns to its original shape after the load is removed).
At near-zero stress and strain, the stress–strain curve is linear, and the relationship between stress and strain is described by Hooke's law that states stress is proportional to strain. The coefficient of proportionality is Young's modulus. The higher the modulus, the more stress is needed to create the same amount of strain; an idealized rigid body would have an infinite Young's modulus.
Not many materials are linear and elastic beyond a small amount of deformation.[citation needed]
Formula and units[edit]
, where[2]
- is Young's modulus
- is the uniaxial stress, or uniaxial force per unit surface
- is the strain, or proportional deformation (change in length divided by original length); it is dimensionless
Both and have units of pressure, while is dimensionless. Young's moduli are typically so large that they are expressed not in pascals but in megapascals (MPa or N/mm2) or gigapascals (GPa or kN/mm2).
Not to be confused with[edit]
Material stiffness should not be confused with these properties:
- Strength: maximal amount of stress the material can withstand while staying in the elastic (reversible) deformation regime;
- Geometric stiffness: a global characteristic of the body that depends on its shape, and not only on the local properties of the material; for instance, an I-beam has a higher bending stiffness than a rod of the same material for a given mass per length;
- Hardness: relative resistance of the material's surface to penetration by a harder body;
- Toughness: amount of energy that a material can absorb before fracture.
Usage[edit]
Young's modulus enables the calculation of the change in the dimension of a bar made of an isotropic elastic material under tensile or compressive loads. For instance, it predicts how much a material sample extends under tension or shortens under compression. The Young's modulus directly applies to cases of uniaxial stress, that is tensile or compressive stress in one direction and no stress in the other directions. Young's modulus is also used in order to predict the deflection that will occur in a statically determinatebeam when a load is applied at a point in between the beam's supports. Other elastic calculations usually require the use of one additional elastic property, such as the shear modulus, bulk modulus or Poisson's ratio. Any two of these parameters are sufficient to fully describe elasticity in an isotropic material.
Linear versus non-linear[edit]
Young's modulus represents the factor of proportionality in Hooke's law, which relates the stress and the strain. However, Hooke's law is only valid under the assumption of an elastic and linear response. Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however all solid materials exhibit nearly Hookean behavior for small enough strains or stresses. If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear. Otherwise (if the typical stress one would apply is outside the linear range) the material is said to be non-linear.
Steel, carbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear. However, this is not an absolute classification: if very small stresses or strains are applied to a non-linear material, the response will be linear, but if very high stress or strain is applied to a linear material, the linear theory will not be enough. For example, as the linear theory implies reversibility, it would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure.
In solid mechanics, the slope of the stress–strain curve at any point is called the tangent modulus. It can be experimentally determined from the slope of a stress–strain curve created during tensile tests conducted on a sample of the material.
Directional materials[edit]
Young's modulus is not always the same in all orientations of a material. Most metals and ceramics, along with many other materials, are isotropic, and their mechanical properties are the same in all orientations. However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional. These materials then become anisotropic, and Young's modulus will change depending on the direction of the force vector. Anisotropy can be seen in many composites as well. For example, carbon fiber has a much higher Young's modulus (is much stiffer) when force is loaded parallel to the fibers (along the grain). Other such materials include wood and reinforced concrete. Engineers can use this directional phenomenon to their advantage in creating structures.
Calculation[edit]
Young's modulus E, can be calculated by dividing the tensile stress,, by the engineering extensional strain, , in the elastic (initial, linear) portion of the physical stress–strain curve:
where
- E is the Young's modulus (modulus of elasticity)
- F is the force exerted on an object under tension;
- A is the actual cross-sectional area, which equals the area of the cross-section perpendicular to the applied force;
- ΔL is the amount by which the length of the object changes (ΔL is positive if the material is stretched , and negative when the material is compressed);
- L0 is the original length of the object.
Force exerted by stretched or contracted material[edit]
The Young's modulus of a material can be used to calculate the force it exerts under specific strain.
where F is the force exerted by the material when contracted or stretched by .
Hooke's law for a stretched wire can be derived from this formula:
where it comes in saturation
- and
But note that the elasticity of coiled springs comes from shear modulus, not Young's modulus.
Elastic potential energy[edit]
The elastic potential energy stored in a linear elastic material is given by the integral of the Hooke's law:
now by explicating the intensive variables:
This means that the elastic potential energy density (i.e., per unit volume) is given by:
or, in simple notation, for a linear elastic material:, since the strain is defined .
In a nonlinear elastic material the Young's modulus is a function of the strain, so the second equivalence no longer holds and the elastic energy is not a quadratic function of the strain:
Relation among elastic constants[edit]
For homogeneous isotropic materials simple relations exist between elastic constants (Young's modulus E, shear modulusG, bulk modulusK, and Poisson's ratioν) that allow calculating them all as long as two are known:
Temperature Dependence[edit]
The Young's modulus of metals varies with the temperature and can be realized through the change in the interatomic bonding of the atoms and hence its change is found to be dependent on the change in the work function of the metal. Although classically, this change is predicted through fitting and without a clear underlying mechanism (e.g. the Watchman's formula), the Rahemi-Li model[3] demonstrates how the change in the electron work function leads to change in the Young's modulus of metals and predicts this variation with calculable parameters, using the generalization of the Lennard-Jones potential to solids. In general, as the temperature increases, the Young's modulus decreases viaWhere the electron work function varies with the temperature as and is a calculable material property which is dependent on the crystal structure (e.g. BCC,FCC,etc.). is the electron work function at T=0 and is constant throughout the change.
Approximate values[edit]
Influences of selected glass component additions on Young's modulus of a specific base glass
Young's modulus can vary somewhat due to differences in sample composition and test method. The rate of deformation has the greatest impact on the data collected, especially in polymers. The values here are approximate and only meant for relative comparison.
Material | GPa | |
---|---|---|
Rubber (small strain) | 0.01–0.1[4] | 1.45–14.5×10−3 |
Low-density polyethylene[5] | 0.11–0.86 | 1.6–6.5×10−2 |
Diatomfrustules (largely silicic acid)[6] | 0.35–2.77 | 0.05–0.4 |
PTFE (Teflon) | 0.5[4] | 0.075 |
HDPE | 0.8 | 0.116 |
Bacteriophage capsids[7] | 1–3 | 0.15–0.435 |
Polypropylene | 1.5–2[4] | 0.22–0.29 |
Polycarbonate | 2–2.4 | 0.29-0.36 |
Polyethylene terephthalate (PET) | 2–2.7[4] | 0.29–0.39 |
Nylon | 2–4 | 0.29–0.58 |
Polystyrene, solid | 3–3.5[4] | 0.44–0.51 |
Polystyrene, foam[8] | 0.0025–0.007 | 0.00036–0.00102 |
Medium-density fiberboard (MDF)[9] | 4 | 0.58 |
Wood (along grain) | 11[4] | 1.60 |
Human Cortical Bone[10] | 14 | 2.03 |
Glass-reinforced polyester matrix[11] | 17.2 | 2.49 |
Aromatic peptide nanotubes[12][13] | 19–27 | 2.76–3.92 |
High-strength concrete | 30[4] | 4.35 |
Amino-acid molecular crystals[14] | 21–44 | 3.04–6.38 |
Carbon fiber reinforced plastic (50/50 fibre/matrix, biaxial fabric) | 30–50[15] | 4.35–7.25 |
Hemp fiber[16] | 35 | 5.08 |
Magnesiummetal (Mg) | 45[4] | 6.53 |
Glass (see chart)[specify] | 50–90[4] | 7.25–13.1 |
Flax fiber[17] | 58 | 8.41 |
Aluminum | 69[4] | 10 |
Mother-of-pearl (nacre, largely calcium carbonate)[18] | 70 | 10.2 |
Aramid[19] | 70.5–112.4 | 10.2–16.3 |
Tooth enamel (largely calcium phosphate)[20] | 83 | 12 |
Stinging nettle fiber[21] | 87 | 12.6 |
Bronze | 96–120[4] | 13.9–17.4 |
Brass | 100–125[4] | 14.5–18.1 |
Titanium (Ti) | 110.3 | 16[4] |
Titanium alloys | 105–120[4] | 15–17.5 |
Copper (Cu) | 117 | 17 |
Carbon fiber reinforced plastic (70/30 fibre/matrix, unidirectional, along fibre)[22] | 181 | 26.3 |
Silicon Single crystal, different directions[23][24] | 130–185 | 18.9–26.8 |
Wrought iron | 190–210[4] | 27.6–30.5 |
Steel (ASTM-A36) | 200[4] | 29 |
polycrystalline Yttrium iron garnet (YIG)[25] | 193 | 28 |
single-crystal Yttrium iron garnet (YIG)[26] | 200 | 29 |
Cobalt-chrome (CoCr)[27] | 220–258 | 29 |
Aromatic peptide nanospheres[28] | 230–275 | 33.4–40 |
Beryllium (Be)[29] | 287 | 41.6 |
Molybdenum (Mo) | 329–330[4][30][31] | 47.7–47.9 |
Tungsten (W) | 400–410[4] | 58–59 |
Silicon carbide (SiC) | 450[4] | 65 |
Tungsten carbide (WC) | 450–650[4] | 65–94 |
Osmium (Os) | 525–562[32] | 76.1–81.5 |
Single-walled carbon nanotube | 1,000+[33][34] | 150+ |
Graphene (C) | 1050[35] | 152 |
Diamond (C) | 1050–1210[36] | 152–175 |
Carbyne (C)[37] | 32100[38] | 4,660 |
See also[edit]
References[edit]
- ^The Rational mechanics of Flexible or Elastic Bodies, 1638–1788: Introduction to Leonhardi Euleri Opera Omnia, vol. X and XI, Seriei Secundae. Orell Fussli.
- ^IUPAC, Compendium of Chemical Terminology, 2nd ed. (the 'Gold Book') (1997). Online corrected version: (2006–) 'modulus of elasticity (Young's modulus), E'. doi:10.1351/goldbook.M03966
- ^Rahemi, Reza; Li, Dongyang (April 2015). 'Variation in electron work function with temperature and its effect on the Young's modulus of metals'. Scripta Materialia. 99 (2015): 41–44. arXiv:1503.08250. doi:10.1016/j.scriptamat.2014.11.022.
- ^ abcdefghijklmnopqrst'Elastic Properties and Young Modulus for some Materials'. The Engineering ToolBox. Retrieved January 6, 2012.
- ^'Overview of materials for Low Density Polyethylene (LDPE), Molded'. Matweb. Archived from the original on January 1, 2011. Retrieved February 7, 2013.
- ^Subhash G, Yao S, Bellinger B, Gretz MR (2005). 'Investigation of mechanical properties of diatom frustules using nanoindentation'. J Nanosci Nanotechnol. 5 (1): 50–6. doi:10.1166/jnn.2005.006. PMID15762160.
- ^Ivanovska IL, de Pablo PJ, Sgalari G, MacKintosh FC, Carrascosa JL, Schmidt CF, Wuite GJ (2004). 'Bacteriophage capsids: Tough nanoshells with complex elastic properties'. Proc Natl Acad Sci USA. 101 (20): 7600–5. Bibcode:2004PNAS.101.7600I. doi:10.1073/pnas.0308198101. PMC419652. PMID15133147.
- ^'Styrodur Technical Data'(PDF). BASF. Retrieved March 15, 2016.
- ^'Medium Density Fiberboard (MDF) Material Properties :: MakeItFrom.com'. Retrieved February 4, 2016.
- ^Rho, JY (1993). 'Young's modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements'. Journal of Biomechanics. 26 (2): 111–119. doi:10.1016/0021-9290(93)90042-d. PMID8429054.
- ^'Polyester Matrix Composite reinforced by glass fibers (Fiberglass)'. [SubsTech] (2008-05-17). Retrieved on 2011-03-30.
- ^Kol, N.; et al. (June 8, 2005). 'Self-Assembled Peptide Nanotubes Are Uniquely Rigid Bioinspired Supramolecular Structures'. Nano Letters. 5 (7): 1343–1346. Bibcode:2005NanoL..5.1343K. doi:10.1021/nl0505896.
- ^Niu, L.; et al. (June 6, 2007). 'Using the Bending Beam Model to Estimate the Elasticity of Diphenylalanine Nanotubes'. Langmuir. 23 (14): 7443–7446. doi:10.1021/la7010106. PMID17550276.
- ^Azuri, I.; et al. (November 9, 2015). 'Unusually Large Young's Moduli of Amino Acid Molecular Crystals'. Angew. Chem. Int. Ed. 54 (46): 13566–13570. doi:10.1002/anie.201505813. PMID26373817.
- ^'Composites Design and Manufacture (BEng) – MATS 324'.
- ^Nabi Saheb, D.; Jog, JP. (1999). 'Natural fibre polymer composites: a review'. Advances in Polymer Technology. 18 (4): 351–363. doi:10.1002/(SICI)1098-2329(199924)18:4<351::AID-ADV6>3.0.CO;2-X.
- ^Bodros, E. (2002). 'Analysis of the flax fibres tensile behaviour and analysis of the tensile stiffness increase'. Composite Part A. 33 (7): 939–948. doi:10.1016/S1359-835X(02)00040-4.
- ^A. P. Jackson,J. F. V. Vincent and R. M. Turner (1988). 'The Mechanical Design of Nacre'. Proceedings of the Royal Society B. 234 (1277): 415–440. Bibcode:1988RSPSB.234.415J. doi:10.1098/rspb.1988.0056.
- ^DuPont (2001). 'Kevlar Technical Guide': 9.
- ^M. Staines, W. H. Robinson and J. A. A. Hood (1981). 'Spherical indentation of tooth enamel'. Journal of Materials Science. 16 (9): 2551–2556. Bibcode:1981JMatS.16.2551S. doi:10.1007/bf01113595.
- ^Bodros, E.; Baley, C. (May 15, 2008). 'Study of the tensile properties of stinging nettle fibres (Urtica dioica)'. Materials Letters. 62 (14): 2143–2145. CiteSeerX10.1.1.299.6908. doi:10.1016/j.matlet.2007.11.034.
- ^Epoxy Matrix Composite reinforced by 70% carbon fibers [SubsTech]. Substech.com (2006-11-06). Retrieved on 2011-03-30.
- ^'Physical properties of Silicon (Si)'. Ioffe Institute Database. Retrieved on 2011-05-27.
- ^E.J. Boyd; et al. (February 2012). 'Measurement of the Anisotropy of Young's Modulus in Single-Crystal Silicon'. Journal of Microelectromechanical Systems. 21 (1): 243–249. doi:10.1109/JMEMS.2011.2174415.
- ^Chou, H. M.; Case, E. D. (November 1988). 'Characterization of some mechanical properties of polycrystalline yttrium iron garnet (YIG) by non-destructive methods'. Journal of Materials Science Letters. 7 (11): 1217–1220. doi:10.1007/BF00722341.
- ^YIG properties
- ^'Properties of cobalt-chrome alloys – Heraeus Kulzer cara'. Archived from the original on July 1, 2015. Retrieved February 4, 2016.
- ^Adler-Abramovich, L.; et al. (December 17, 2010). 'Self-Assembled Organic Nanostructures with Metallic-Like Stiffness'. Angewandte Chemie International Edition. 49 (51): 9939–9942. doi:10.1002/anie.201002037. PMID20878815.
- ^Foley, James C.; et al. (2010). 'An Overview of Current Research and Industrial Practices of Be Powder Metallurgy'. In Marquis, Fernand D.S. (ed.). Powder Materials: Current Research and Industrial Practices III. Hoboken, NJ, USA: John Wiley & Sons, Inc. p. 263. doi:10.1002/9781118984239.ch32. ISBN9781118984239.
- ^'Molybdenum: physical properties'. webelements. Retrieved January 27, 2015.
- ^'Molybdenum, Mo'(PDF). Glemco. Retrieved January 27, 2014.
- ^D.K.Pandey; Singh, D.; Yadawa, P. K.; et al. (2009). 'Ultrasonic Study of Osmium and Ruthenium'(PDF). Platinum Metals Rev. 53 (4): 91–97. doi:10.1595/147106709X430927. Retrieved November 4, 2014.
- ^L. Forro; et al. 'Electronic and mechanical properties of carbon nanotubes'(PDF).
- ^Y. H. Yang; Li, W. Z.; et al. (2011). 'Radial elasticity of single-walled carbon nanotube measured by atomic force microscopy'. Applied Physics Letters. 98 (4): 041901. Bibcode:2011ApPhL.98d1901Y. doi:10.1063/1.3546170.
- ^Fang Liu; Pingbing Ming & Ju Li. 'Ab initio calculation of ideal strength and phonon instability of graphene under tension'(PDF).
- ^Spear and Dismukes (1994). Synthetic Diamond – Emerging CVD Science and Technology. Wiley, N.Y. p. 315. ISBN978-0-471-53589-8.
- ^Owano, Nancy (August 20, 2013). 'Carbyne is stronger than any known material'. phys.org.
- ^Liu, Mingjie; Artyukhov, Vasilii I; Lee, Hoonkyung; Xu, Fangbo; Yakobson, Boris I (2013). 'Carbyne From First Principles: Chain of C Atoms, a Nanorod or a Nanorope?'. ACS Nano. 7 (11): 10075–10082. arXiv:1308.2258. doi:10.1021/nn404177r. PMID24093753.
Further reading[edit]
- ASTM E 111, 'Standard Test Method for Young's Modulus, Tangent Modulus, and Chord Modulus'
- The ASM Handbook (various volumes) contains Young's Modulus for various materials and information on calculations. Online version(subscription required)
External links[edit]
Conversion formulae | |||||||
---|---|---|---|---|---|---|---|
Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these; thus, given any two, any other of the elastic moduli can be calculated according to these formulas. | |||||||
Notes | |||||||
There are two valid solutions. The minus sign leads to .The plus sign leads to . | |||||||
Cannot be used when | |||||||
Retrieved from 'https://en.wikipedia.org/w/index.php?title=Young%27s_modulus&oldid=902492741'
Young's Modulus or Tensile Modulus alt. Modulus of Elasticity - and Ultimate Tensile and Yield Strength for steel, glass, wood and other common materials
Tensile Modulus - or Young's Modulus alt. Modulus of Elasticity - is a measure of stiffness of an elastic material. It is used to describe the elastic properties of objects like wires, rods or columns when they are stretched or compressed.
Tensile Modulus is defined as the
'ratio of stress (force per unit area) along an axis to strain (ratio of deformation over initial length) along that axis'
I personally cannot replicate it.The user emailed me their IPS file. This is the output after I've loaded it in Organiser, and right clicked, selected Re-symbolicate:I assume this is where the problem occurred in my code: 3 FlightMachine 0x03b970 0x100028000 + 802404 FlightMachine 0x08b79c 0x100028000 + 407452But how do I find out what is at 0x100028000 + 80240, to find out what the actual problem is?Thank you. What is ips file in ios. I'm trying to find out why my app is crashing for certain users.
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It can be used to predict the elongation or compression of an object as long as the stress is less than the yield strength of the material. More about the definitions below the table.
Material | Tensile Modulus (Young's Modulus, Modulus of Elasticity) - E - | Ultimate Tensile Strength - σu - (MPa) | Yield Strength - σy - (MPa) | |
---|---|---|---|---|
(106 psi) | (GPa) | |||
ABS plastics | 1.4 - 3.1 | 40 | ||
A53 Seamless and Welded Standard Steel Pipe - Grade A | 331 | 207 | ||
A53 Seamless and Welded Standard Steel Pipe - Grade B | 414 | 241 | ||
A106 Seamless Carbon Steel Pipe - Grade A | 400 | 248 | ||
A106 Seamless Carbon Steel Pipe - Grade B | 483 | 345 | ||
A106 Seamless Carbon Steel Pipe - Grade C | 483 | 276 | ||
A252 Piling Steel Pipe - Grade 1 | 345 | 207 | ||
A252 Piling Steel Pipe - Grade 2 | 414 | 241 | ||
A252 Piling Steel Pipe - Grade 3 | 455 | 310 | ||
A501 Hot Formed Carbon Steel Structural Tubing - Grade A | 400 | 248 | ||
A501 Hot Formed Carbon Steel Structural Tubing - Grade B | 483 | 345 | ||
A523 Cable Circuit Steel Piping - Grade A | 331 | 207 | ||
A523 Cable Circuit Steel Piping - Grade B | 414 | 241 | ||
A618 Hot-Formed High-Strength Low-Alloy Structural Tubing - Grade Ia & Ib | 483 | 345 | ||
A618 Hot-Formed High-Strength Low-Alloy Structural Tubing - Grade II | 414 | 345 | ||
A618 Hot-Formed High-Strength Low-Alloy Structural Tubing - Grade III | 448 | 345 | ||
API 5L Line Pipe | 310 - 1145 | 175 - 1048 | ||
Acetals | 2.8 | 65 | ||
Acrylic | 3.2 | 70 | ||
Aluminum Bronze | 120 | |||
Aluminum | 10.0 | 69 | 110 | 95 |
Aluminum Alloys | 10.2 | |||
Antimony | 11.3 | |||
Aramid | 70 - 112 | |||
Beryllium (Be) | 42 | 287 | ||
Beryllium Copper | 18.0 | |||
Bismuth | 4.6 | |||
Bone, compact | 18 | 170 (compression) | ||
Bone, spongy | 76 | |||
Boron | 3100 | |||
Brass | 102 - 125 | 250 | ||
Brass, Naval | 100 | |||
Bronze | 96 - 120 | |||
CAB | 0.8 | |||
Cadmium | 4.6 | |||
Carbon Fiber Reinforced Plastic | 150 | |||
Carbon nanotube, single-walled | 1000+ | |||
Cast Iron 4.5% C, ASTM A-48 | 170 | |||
Cellulose, cotton, wood pulp and regenerated | 80 - 240 | |||
Cellulose acetate, molded | 12 - 58 | |||
Cellulose acetate, sheet | 30 - 52 | |||
Cellulose nitrate, celluloid | 50 | |||
Chlorinated polyether | 1.1 | 39 | ||
Chlorinated PVC (CPVC) | 2.9 | |||
Chromium | 36 | |||
Cobalt | 30 | |||
Concrete | 17 | |||
Concrete, High Strength (compression) | 30 | 40 (compression) | ||
Copper | 17 | 117 | 220 | 70 |
Diamond (C) | 1220 | |||
Douglas fir Wood | 13 | 50 (compression) | ||
Epoxy resins | 3-2 | 26 - 85 | ||
Fiberboard, Medium Density | 4 | |||
Flax fiber | 58 | |||
Glass | 50 - 90 | 50 (compression) | ||
Glass reinforced polyester matrix | 17 | |||
Gold | 10.8 | 74 | ||
Granite | 52 | |||
Graphene | 1000 | |||
Grey Cast Iron | 130 | |||
Hemp fiber | 35 | |||
Inconel | 31 | |||
Iridium | 75 | |||
Iron | 28.5 | 210 | ||
Lead | 2.0 | |||
Magnesium metal (Mg) | 6.4 | 45 | ||
Manganese | 23 | |||
Marble | 15 | |||
MDF - Medium-density fiberboard | 4 | |||
Mercury | ||||
Molybdenum (Mo) | 40 | 329 | ||
Monel Metal | 26 | |||
Nickel | 31 | 170 | ||
Nickel Silver | 18.5 | |||
Nickel Steel | 29 | |||
Niobium (Columbium) | 15 | |||
Nylon-6 | 2 - 4 | 45 - 90 | 45 | |
Nylon-66 | 60 - 80 | |||
Oak Wood (along grain) | 11 | |||
Osmium (Os) | 80 | 550 | ||
Phenolic cast resins | 33 - 59 | |||
Phenol-formaldehyde molding compounds | 45 - 52 | |||
Phosphor Bronze | 116 | |||
Pine Wood (along grain) | 9 | 40 | ||
Platinum | 21.3 | |||
Plutonium | 14 | 97 | ||
Polyacrylonitrile, fibers | 200 | |||
Polybenzoxazole | 3.5 | |||
Polycarbonates | 2.6 | 52 - 62 | ||
Polyethylene HDPE (high density) | 0.8 | 15 | ||
Polyethylene Terephthalate, PET | 2 - 2.7 | 55 | ||
Polyamide | 2.5 | 85 | ||
Polyisoprene, hard rubber | 39 | |||
Polymethylmethacrylate (PMMA) | 2.4 - 3.4 | |||
Polyimide aromatics | 3.1 | 68 | ||
Polypropylene, PP | 1.5 - 2 | 28 - 36 | ||
Polystyrene, PS | 3 - 3.5 | 30 - 100 | ||
Polyethylene, LDPE (low density) | 0.11 - 0.45 | |||
Polytetrafluoroethylene (PTFE) | 0.4 | |||
Polyurethane cast liquid | 10 - 20 | |||
Polyurethane elastomer | 29 - 55 | |||
Polyvinylchloride (PVC) | 2.4 - 4.1 | |||
Potassium | ||||
Rhodium | 42 | |||
Rubber, small strain | 0.01 - 0.1 | |||
Sapphire | 435 | |||
Selenium | 8.4 | |||
Silicon | 16 | 130 - 185 | ||
Silicon Carbide | 450 | 3440 | ||
Silver | 10.5 | |||
Sodium | ||||
Steel, High Strength Alloy ASTM A-514 | 760 | 690 | ||
Steel, stainless AISI 302 | 180 | 860 | 502 | |
Steel, Structural ASTM-A36 | 29 | 200 | 400 | 250 |
Tantalum | 27 | |||
Thorium | 8.5 | |||
Tin | 47 | |||
Titanium | 16 | |||
Titanium Alloy | 105 - 120 | 900 | 730 | |
Tooth enamel | 83 | |||
Tungsten (W) | 400 - 410 | |||
Tungsten Carbide (WC) | 450 - 650 | |||
Uranium | 24 | 170 | ||
Vanadium | 19 | |||
Wrought Iron | 190 - 210 | |||
Wood | ||||
Zinc | 12 |
- 1 Pa (N/m2) = 1x10-6 N/mm2 = 1.4504x10-4 psi
- 1 MPa = 106 N/m2 = 0.145x103 psi (lbf/in2) = 0.145 ksi
- 1 GPa = 109 N/m2= 106 N/cm2= 103 N/mm2 = 0.145x106 psi (lbf/in2)
- 1 psi (lb/in2) = 0.001 ksi = 144 psf (lbf/ft2) = 6,894.8 Pa (N/m2) = 6.895x10-3 N/mm2
Note! - this online pressure converter can be used to convert between units of Tensile modulus.
Strain - ε
Strain is the 'deformation of a solid due to stress' - change in dimension divided by the original value of the dimension - and can be expressed as
ε = dL / L (1)
where
ε = strain (m/m, in/in)
dL = elongation or compression (offset) of object (m, in)
L = length of object (m, in)
Stress - σ
Stress is force per unit area and can be expressed as
σ = F / A (2)
where
σ = stress (N/m2, lb/in2, psi)
F = applied force (N, lb)
A = stress area of object (m2, in2)
- tensile stress - stress that tends to stretch or lengthen the material - acts normal to the stressed area
- compressible stress - stress that tends to compress or shorten the material - acts normal to the stressed area
- shearing stress - stress that tends to shear the material - acts in plane to the stressed area at right-angles to compressible or tensile stress
Young's Modulus - Tensile Modulus, Modulus of Elasticity - E
Young's modulus can be expressed as
Modulus Of Elasticity Equation
E = stress / strain
= σ / ε
= (F / A) / (dL / L) (3)
where
E = Young's Modulus of Elasticity (N/m2, lb/in2, psi)
- named after the 18th-century English physician and physicist Thomas Young
Elasticity
Elasticity is a property of an object or material indicating how it will restore it to its original shape after distortion.
A spring is an example of an elastic object - when stretched, it exerts a restoring force which tends to bring it back to its original length. This restoring force is in general proportional to the stretch described by Hooke's Law.
Hooke's Law
It takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon the stretching force is called Hooke's law and can be expressed as
Fs = -k dL (4)
where
Fs = force in the spring (N)
k = spring constant (N/m)
dL = elongation of the spring (m)
Note that Hooke's Law can also be applied to materials undergoing three dimensional stress (triaxial loading).
Yield strength - σy
Yield strength is defined in engineering as the amount of stress (Yield point) that a material can undergo before moving from elastic deformation into plastic deformation.
- Yielding - a material deforms permanently
The Yield Point is in mild- or medium-carbon steel the stress at which a marked increase in deformation occurs without increase in load. In other steels and in nonferrous metals this phenomenon is not observed.
Ultimate Tensile Strength - σu
The Ultimate Tensile Strength - UTS - of a material is the limit stress at which the material actually breaks, with a sudden release of the stored elastic energy.
Related Topics
- Mechanics - Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more
- Material Properties - Material properties for gases, fluids and solids - densities, specific heats, viscosities and more
- Statics - Loads - force and torque, beams and columns
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